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arXiv · 2205.08302

Gauss-Manin connection in disguise: Open Gromov-Witten invariants

Felipe Espreafico
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Abstract

In mirror symmetry, after the work by J. Walcher, the number of holomorphic disks with boundary on the real quintic lagrangian in a general quintic threefold is related to the periods of the mirror quintic family with boundary on two homologous rational curves. Following the ideias of H.Movasati, we construct a quasi-affine space parametrizing such objects enhanced with a frame for the relative de Rham cohomology with boundary at the curves compatible with the mixed Hodge structure. We also compute a modular vector field attached to such a parametrization.

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Felipe Espreafico. 2022-05-17. Gauss-Manin connection in disguise: Open Gromov-Witten invariants. https://arxiv.org/abs/2205.08302

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